Stable cylindrical Lévy processes and the stochastic Cauchy problem

Electronic Communications in Probability

Markus Riedle¹ 

关键词: cylindrical Lèvy processes;    stochastic partial differential equations;    stable distributions;   

DOI  :  10.1214/18-ECP134

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

In this work, we consider the stochastic Cauchy problem driven by the canonical $\alpha $-stable cylindrical Lévy process. This noise naturally generalises the cylindrical Brownian motion or space-time Gaussian white noise. We derive a sufficient and necessary condition for the existence of the weak and mild solution of the stochastic Cauchy problem and establish the temporal irregularity of the solution.

【 授权许可】

CC BY